Precalculus with Limits: A Graphing Approach
Precalculus with Limits: A Graphing Approach
7th Edition
ISBN: 9781305071711
Author: Ron Larson
Publisher: Brooks/Cole
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Chapter 5.4, Problem 49E
To determine

To find: the exact value of the trigonometric expression when sinu=−725 and cosv=−45 .

Expert Solution & Answer
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Answer to Problem 49E

  sin(u−v)=−44125 .

Explanation of Solution

Given information:

Given expression,

  cos(u−v)

Calculation:

Consider that sinu=−725 and cosv=−45 , u and v are in quadrant III.

The sine of an angle is equal to opposite side over the hypotenuse. Since sinu=−725 and u is quadrant III. So, the following figure will obtain:

  Precalculus with Limits: A Graphing Approach, Chapter 5.4, Problem 49E , additional homework tip 1

Since cosine of an angle is equal to adjacent side over the hypotenuse and u is in quadrant III.

Therefore:

  cosu=−2425

Since, cosv=−45 and v is in quadrant III. Consider the following figure:

  Precalculus with Limits: A Graphing Approach, Chapter 5.4, Problem 49E , additional homework tip 2

Since the side of an angle is equal to opposite side over the hypotenuse. Therefore:

  sinv=−35

Apply the difference formula for sine that is:

  sin(u−v)=sinucosv−cosusinv

Substitute:

  sinu=−725,cosu=−2425,sinv=−35

And,

  cosv=−45

So,

  sin(u−v)=(−725)(−45)−(−35)(−2425)=28125−72125=−44125

Therefore,

  sin(u−v)=−44125 .

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Chapter 5.4, Problem 48E
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Chapter 5.4, Problem 50E

Chapter 5 Solutions

Precalculus with Limits: A Graphing Approach

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